Statistics and
Probability
Quarter 3 – Module 1:
Random Variables and
Probability Distributions
Statistics and Probability
Alternative Delivery Mode
Quarter 3 – Module 1: Random Variables and Probability Distributions
First Edition, 2020
Republic Act 8293, section 176 states that: No copyright shall subsist in any work of
the Government of the Philippines. However, prior approval of the government agency or office
wherein the work is created shall be necessary for exploitation of such work for profit. Such
agency or office may, among other things, impose as a condition the payment of royalties.
Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names,
trademarks, etc.) included in this module are owned by their respective copyright holders.
Every effort has been exerted to locate and seek permission to use these materials from their
respective copyright owners. The publisher and authors do not represent nor claim ownership
over them.
Published by the Department of Education
Secretary: Leonor Magtolis Briones
Undersecretary: Diosdado M. San Antonio
SENIOR HS MODULE DEVELOPMENT TEAM
AUTHOR
Co-Author – Language Editor
Co-Author – Content Evaluator
Co-Author – Illustrator
Co-Author – Layout Artist
: Chelsea Mae B. Brofar
: Mee Ann Mae Loria - Tungol
: Haren B. Valencia
: Chelsea Mae B. Brofar
: Chelsea Mae B. Brofar
TEAM LEADERS
School Head
LRMDS Coordinator
: Reycor E. Sacdalan, PhD
: Pearly V. Villagracia
SDO-BATAAN MANAGEMENT TEAM
Schools Division Superintendent
OIC- Asst. Schools Division Superintendent
Chief Education Supervisor, CID
Education Program Supervisor, LRMDS
Education Program Supervisor, AP/ADM
Education Program Supervisor, Senior HS
Project Development Officer II, LRMDS
Division Librarian II, LRMDS
: Romeo M. Alip, PhD, CESO V
: William Roderick R. Fallorin, CESE
: Milagros M. Peñaflor, PhD
: Edgar E. Garcia, MITE
: Romeo M. Layug
: Danilo C. Caysido
: Joan T. Briz
: Rosita P. Serrano
REGIONAL OFFICE 3 MANAGEMENT TEAM
Regional Director
Chief Education Supervisor, CLMD
Education Program Supervisor, LRMS
Education Program Supervisor, ADM
: May B. Eclar, PhD, CESO III
: Librada M. Rubio, PhD
: Ma. Editha R. Caparas, EdD
: Nestor P. Nuesca, EdD
Statistics and
Probability
Quarter 3 – Module 1:
Random Variables and
Probability Distributions
Introductory Message
This Self-Learning Module (SLM) is prepared so that you, our dear learners,
can continue your studies and learn while at home. Activities, questions, directions,
exercises, and discussions are carefully stated for you to understand each lesson.
Each SLM is composed of different parts. Each part shall guide you step-bystep as you discover and understand the lesson prepared for you.
Pre-tests are provided to measure your prior knowledge on lessons in each
SLM. This will tell you if you need to proceed on completing this module or if you
need to ask your facilitator or your teacher’s assistance for better understanding of
the lesson. At the end of each module, you need to answer the post-test to self-check
your learning. Answer keys are provided for each activity and test. We trust that you
will be honest in using these.
In addition to the material in the main text, Notes to the Teacher are also
provided to our facilitators and parents for strategies and reminders on how they can
best help you on your home-based learning.
Please use this module with care. Do not put unnecessary marks on any part
of this SLM. Use a separate sheet of paper in answering the exercises and tests. And
read the instructions carefully before performing each task.
If you have any questions in using this SLM or any difficulty in answering the
tasks in this module, do not hesitate to consult your teacher or facilitator.
Thank you.
What I Need to Know
After going through this module, you are expected to:
1. Illustrate a random variable (discrete or continuous). M11/12SP-IIIa-1
2. Distinguish between a discrete and continuous random variable. M11/12SPIIIa-2
3. Find possible values of a random variable. M11/12SP-IIIa-3
4. Illustrate a probability distribution for a discrete random variable and its
properties. M11/12SP-IIIa-4
5. Compute probabilities corresponding to a given random variable. M11/12SPIIIa-6
1
What I Know
DIRECTION: Write your answer on a separate sheet of paper.
A. Read the statements carefully and choose the letter of the best
answer.
1. If two coins are tossed once, which is NOT a possible value of the random
variable for the number of heads?
A. 0
B. 1
C. 2
D. 3
2. Which of the following is a discrete random variable?
A. Length of wire ropes
B. Number of soldiers in the troop
C. Amount of paint used in repainting the building
D. Voltage of car batteries
3. Which formula gives the probability distribution shown by the table?
X
3
4
5
P(X)
1/3
1/4
1/5
A.
B.
C.
D.
P(X)
P(X)
P(X)
P(X)
=
=
=
=
X
1/X
X/3
X/5
4. How many ways are there in tossing two coins once?
A.
B.
C.
D.
5. It is a
A.
B.
C.
D.
4
3
2
1
numerical quantity that is assigned to the outcome of an experiment.
random variable
variable
probability
probability distribution
2
B. Classify the following random variables as discrete or continuous.
1.
2.
3.
4.
The
The
The
The
5. The
weight of the professional wrestlers
number of winners in lotto for each day
area of lots in an exclusive subdivision
speed of a car
number of dropouts in a school per district
C. Determine the values of the random variables in each of the following
distributions.
1. Two coins are tossed. Let T be the number of tails that occur. Determine
the values of the random variable T.
2. A meeting of envoys was attended by 4 Koreans and 2 Filipinos. If three
envoys were selected at random one after the other, determine the values
of the random variable F representing the number of Filipinos.
3
Lesson
1
Random Variables and
Probability Distribution
You have learned in your past lessons in junior high school Mathematics that
an experiment or trial is any procedure or activity that can be done repeatedly under
similar conditions. The set of all possible outcomes in an experiment is called the
sample space. The concept of probability distribution is very important in analyzing
statistical data especially in hypothesis testing.
In this lesson, you will explore and understand the random variable.
Before we discuss probability distribution, it is necessary to study first the
concept of random variable. Try to do the next activity to prepare you for this lesson.
Stay focused.
What’s In
A. Identify the term being described in each of the following:
1. Any activity which can be done repeatedly under similar conditions
2. The set of all possible outcomes in an experiment
3. A subset of a sample space
4. The elements in a sample space
5. The ratio of the number of favorable outcomes to the number of possible
outcomes
B. Answer the following questions.
1. In how many ways can two coins fall?
2. If three coins are tossed, in how many ways can they fall?
3. In how many ways can a die fall?
4. In how many ways can two dice fall?
5. How many ways are there in tossing one coin and rolling a die?
Notes to the Teacher
This part aims to assess if the students have prior
knowledge about the topic. Also, it prepares the students to
absorb the lesson.
4
What’s New
Mary Ann, Hazel, and Analyn want to know what numbers can be assigned for
the frequency of heads that will occur in tossing three coins. Can you help
them? Thanks!
The answer in this question requires an understanding of random variables.
You can do it! Aja!
Definitions of Random Variable
A random variable is a result of chance event, that you can measure or
count.
A random variable is a numerical quantity that is assigned to the
outcome of an experiment. It is a variable that assumes numerical
values associated with the events of an experiment.
A random variable is a quantitative variable which values depends on
change.
NOTE:
We use capital letters to represent a random variable.
5
Example 1
Suppose two coins are tossed and we are interested to determine the number
of tails that will come out. Let us use T to represent the number of tails that will
come out. Determine the values of the random variable T.
Solution:
Steps
Solution
1. List the sample space
S = {HH, HT, TH, TT}
2. Count the number of tails
in each outcome and
assign this number to this
outcome.
3. Conclusion
Outcome
Number of Tails
(Value of T)
HH
0
HT
1
TH
1
TT
2
The values of the random variable T (number of
tails) in this experiment are 0, 1 and 2.
Example 2
Two balls are drawn in succession without replacement from an urn
containing 5 orange balls and 6 violet balls. Let V be the random variable
representing the number of violet balls. Find the values of the random variable V.
Solution:
Steps
Solution
S = {OO, OV, VO, VV}
1. List the sample space
6
2. Count the number of violet
balls in each outcome and
assign this number to this
outcome.
3. Conclusion
Outcome
Number of Violet
balls
(Value of V)
OO
0
OV
1
VO
1
VV
2
The values of the random variable V (number of
violet balls) in this experiment are 0, 1, and 2.
Example 3
A basket contains 10 red balls and 4 white balls. If three balls are taken from
the basket one after the other, determine the possible values of the random variable
R representing the number of red balls.
Solution:
Steps
1. List the sample space
2. Count the number of red
balls in each outcome and
assign this number to this
outcome.
3. Conclusion
Solution
S = {RRR, RRW, RWR, WRR, WWR, WRW,
RWW, WWW}
Outcome
Number of Red balls
(Value of R)
RRR
3
RRW
2
RWR
2
WRR
2
WWR
1
WRW
1
RWW
1
WWW
0
The values of the random variable R (number of
red balls) in this experiment are 0, 1, 2, and 3.
7
Example 4
Four coins are tossed. Let T be the random variable representing the number
of tails that occur. Find the values of the random variable T.
Solution:
Steps
1. List the sample space
2. Count the number of tails
in each outcome and
assign this number to this
outcome.
3. Conclusion
Solution
S = {HHHH, HHHT, HHTH, HHTT, HTHH,
HTHT, HTTH, HTTT, THHH, THHT, THTH,
THTT, TTHH, TTHT, TTTH, TTTT}
Outcome
Number of tails
(Value of T)
HHHH
0
HHHT
1
HHTH
1
HHTT
2
HTHH
1
HTHT
2
HTTH
2
HTTT
3
THHH
1
THHT
2
THTH
2
THTT
3
TTHH
2
TTHT
3
TTTH
3
TTTT
4
The values of the random variable T (number of
tails) in this experiment are 0, 1, 2, 3, and 4.
8
Example 5
A pair of dice is rolled. Let X be the random variable representing the sum of
the number of dots on the top faces. Find the values of the random variable X.
Solution:
Steps
1. List the sample space
Solution
S=
{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
2. Count the sum of the
number of dots in each
outcome and assign this
number to this outcome.
Outcome
Sum of the number of
dots
(Value of X)
(1, 1)
2
(1, 2), (2, 1)
3
(1, 3), (3, 1), (2, 2)
4
(1, 4), (4, 1), (2,
3), (3, 2)
5
(1, 5), (5, 1), (2,
4), (4, 2), (3, 3)
6
(1, 6), (6, 1), (2,
5), (5, 2), (4, 3),
(3, 4)
7
(3, 5), (5, 3), (2,
6), (6, 2), (4, 4)
8
(5, 4), (4, 5), (6,
3), (3, 6)
9
(6, 4), (4, 6), (5, 5)
10
(5, 6), (6, 5)
11
(6, 6)
12
9
3. Conclusion
The values of the random variable X (sum of the
number of dots) in this experiment are 2, 4, 5,
6, 7, 8, 9, 10, 11, and 12.
Discrete and Continuous Random Variable
A random variable may be classified as discrete and continuous. A discrete
random variable has a countable number of possible values. A continuous random
variable can assume an infinite number of values in one or more intervals.
Examples:
Discrete Random Variable
Number of pens in a box
Number of ants in a colony
Number of ripe bananas in a basket
Number of COVID 19 positive cases in
Hermosa, Bataan
Number of defective batteries
Continuous Random Variable
Amount of antibiotics in the vial
Length of electric wires
Voltage of car batteries
Weight of newborn in the hospital
Amount of sugar in a cup of coffee
What is It
In the previous grade levels in studying Mathematics, we have learned how to
make a frequency distribution table given a set of raw data. In this part, you will
learn how to construct a probability distribution.
In the previous part of this module, you already learned how to determine the
values of discrete random variable. Constructing a probability distribution is just a
continuation of the previous part. We just need to include an additional step to
illustrate and compute the probabilities corresponding to a given random variable.
Using Example 1 in the previous page,
Steps
Solution
1. List the sample space
S = {HH, HT, TH, TT}
10
2. Count the number of tails
in each outcome and
assign this number to this
outcome.
Outcome
Number of Tails
(Value of T)
HH
0
HT
1
TH
1
TT
2
The values of the random variable T (number of
tails) in this experiment are 0, 1, and 2.
3. Construct the frequency
distribution of the values of
the random variable T.
Number of Tails
Number of
Occurrence
(Value of T)
(Frequency)
4. Construct the probability
distribution of the random
variable T by getting the
probability of occurrence of
each value of the random
variable.
0
1
1
2
2
1
Total
4
Number of
Tails
Number of
Occurrence
Probability
P(T)
(Value of T)
(Frequency)
0
1
1/4
1
2
2/4 or 1/2
2
1
1/4
Total
4
1
The probability distribution of the random
variable T can be written as follows:
T
2
1
0
P(T)
1/4
1/2
1/4
11
4
5. Construct the probability
histogram.
3
2
P(T)
1
0
1
0
2
T
Using Example 2 in the previous page,
Steps
Solution
S = {OO, OV, VO, VV}
1. List the sample space
2. Count the number of violet
balls in each outcome and
assign this number to this
outcome.
Outcome
Number of Violet
Balls
(Value of V)
OO
0
OV
1
VO
1
VV
2
The values of the random variable V (number of
violet balls) in this experiment are 0, 1, and 2.
3. Construct the frequency
distribution of the values of
the random variable V.
Number of Violet
Balls
Number of
Occurrence
(Value of V)
(Frequency)
0
1
1
2
2
1
12
Total
4. Construct the probability
distribution of the random
variable V by getting the
probability of occurrence of
each value of the random
variable.
4
Number of
Violet balls
Number of
Occurrence
Probability
P(V)
(Value of V)
(Frequency)
0
1
1/4
1
2
2/4 or 1/2
2
1
1/4
Total
4
1
The probability distribution of the random
variable V can be written as follows:
V
2
1
0
P(V)
1/4
1/2
1/4
4
5. Construct the probability
histogram.
3
2
P(V)
1
0
0
1
2
V
Using Example 4 in the previous page,
Steps
1. List the sample space
Solution
S = {HHHH, HHHT, HHTH, HHTT, HTHH,
HTHT, HTTH, HTTT, THHH, THHT, THTH,
THTT, TTHH, TTHT, TTTH, TTTT}
13
2. Count the number of tails
in each outcome and
assign this number to this
outcome.
Outcome
Number of tails
(Value of T)
HHHH
0
HHHT
1
HHTH
1
HHTT
2
HTHH
1
HTHT
2
HTTH
2
HTTT
3
THHH
1
THHT
2
THTH
2
THTT
3
TTHH
2
TTHT
3
TTTH
3
TTTT
4
The values of the random variable T (number of
tails) in this experiment are 0, 1, 2, 3, and 4.
3. Construct the frequency
distribution of the values of
the random variable T.
Number of Tails
(Value of T)
Number of
Occurrence
(Frequency)
14
0
1
1
4
2
6
3
4
4
1
Total
16
4. Construct the probability
distribution of the random
variable T by getting the
probability of occurrence of
each value of the random
variable.
Number of
Tails
Number of
Occurrence
Probability
P(T)
(Value of T)
(Frequency)
0
1
1/16
1
4
4/16 or
1/4
2
6
6/16 or
3/8
3
4
4/16 or
1/4
4
1
1/16
Total
16
1
The probability distribution of the random
variable T can be written as follows:
T
0
1
2
3
4
P(T)
1/16
1/4
3/8
1/4
1/16
15
16
5. Construct the probability
histogram.
14
12
10
P(T)
8
6
4
2
0
0
1
2
T
Using Example 5 in the previous page,
Steps
1. List the sample space
Solution
S=
{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
16
3
4
2. Count the sum of the
number of dots in each
outcome and assign
this number to this
outcome.
Outcome
Sum of the
number of
dots
(Value of
X)
(1, 1)
2
(1, 2), (2, 1)
3
(1, 3), (3, 1), (2, 2)
4
(1, 4), (4, 1), (2, 3), (3, 2)
5
(1, 5), (5, 1), (2, 4), (4, 2), (3, 3)
6
(1, 6), (6, 1), (2, 5), (5, 2), (4, 3),
(3, 4)
7
(3, 5), (5, 3), (2, 6), (6, 2), (4, 4)
8
(5, 4), (4, 5), (6, 3), (3, 6)
9
(6, 4), (4, 6), (5, 5)
10
(5, 6), (6, 5)
11
(6, 6)
12
The values of the random variable X (sum of the
number of dots) in this experiment are 2, 3, 4, 5, 6,
7, 8, 9, 10, 11, and 12.
3. Construct the
frequency distribution
of the values of the
random variable X.
Sum of the
number of dots
Number of
Occurrence
(Value of X)
(Frequency)
2
1
3
2
4
3
5
4
6
5
7
6
8
5
9
4
10
3
11
2
17
4. Construct the
probability distribution
of the random variable
X by getting the
probability of
occurrence of each
value of the random
variable.
12
1
Total
36
Sum of the
number of
dots
Number of
Occurrence
Probability P(X)
(Frequency)
(Value of X)
2
1
1/36
3
2
2/36 or 1/18
4
3
3/36 or 1/12
5
4
4/36 or 1/9
6
5
5/36
7
6
6/36 or 1/6
8
5
5/36
9
4
4/36 or 1/9
10
3
3/36 or 1/12
11
2
2/36 or 1/18
12
1
1/36
Total
36
1
The probability distribution of the random variable
X can be written as follows:
X
P(X)
2
3
4
5
6
7
8
9 10 11 12
1 1 1 1 5 1 5 1 1 1 1
36 18 12 9 36 6 36 9 12 18 36
18
36
5. Construct the
probability histogram.
27
P(X)
18
9
0
2
3
4
5
6
7
X
19
8
9 10 11 12
What’s More
Direction: Complete the table below by constructing and illustrating the
probability distribution of Example 3 (refer to page 7).
Steps
Solution
1. List the sample space
2. Count the number of tails
in each outcome and
assign this number to this
outcome.
3. Construct the frequency
distribution of the values of
the given random variable.
4. Construct the probability
distribution of the given
random variable by getting
the probability of
occurrence of each value of
the random variable.
5. Construct the probability
histogram.
What I Have Learned
Direction: Write your answer on a separate sheet of paper.
Answer the following in 2-3 sentences only.
1. How do you describe a discrete random variable?
20
2. How do you describe a continuous random variable?
3. Give three examples of discrete random variable.
4. Give three examples of continuous random variable.
5. What do you notice about the probability values of random variable in each
probability distribution?
6. What is the sum of the probabilities of a random variable?
7. Why should the sum of the probabilities in a probability distribution is always
equal to 1?
8. What is the shape of most probability distributions? Why do you think so?
21
Scoring Rubric
0
No answer at
all
1
Correct
answer but
not in a
sentence
form.
2
Correct
answer
written in a
sentence form
but no
supporting
details.
3
Correct
answer
written in a
sentence form
with 1
supporting
detail from the
text.
4
Correct
answer
written in a
sentence form
with 2 or
more
supporting
detail from
the text.
Did not use
capitalization
and
punctuation.
Used
capitalization
and
punctuation.
Used
capitalization
and
punctuation.
3 or more
spelling
mistakes.
1-2 spelling
mistakes.
All words
spelled
correctly.
What I Can Do
Number of Defective COVID-19 Rapid Antibody Test Kit
Suppose three test kits are tested at random. Let D represent the defective
test kit and let N represent the non-defective test kit. If we let X be the random
variable for the number of defective test kits, construct the probability distribution
of the random variable X.
22
Assessment
DIRECTION: Write your answer on a separate sheet of paper.
A. Multiple Choice. Choose the letter of the best answer.
1. If three coins are tossed, which is NOT a possible value of the random
variable for the number of tails?
A.
B.
C.
D.
1
2
3
4
2. Which of the following is a discrete random variable?
A. Length of electrical wires
B. Number of pencils in a box
C. Amount of sugar used in a cup of coffee
D. Voltage of car batteries
3. Which formula gives the probability distribution shown by the table?
X
3
4
5
P(X)
1/3
¼
1/5
A.
B.
C.
D.
P(X)
P(X)
P(X)
P(X)
=
=
=
=
X
1/X
X/3
X/5
4. How many ways can a "double" come out when you roll two dice?
A.
B.
C.
D.
5. It is a
A.
B.
C.
D.
2
4
6
8
numerical quantity that is assigned to the outcome of an experiment.
random variable
variable
probability
probability distribution
B. Classify the following random variables as discrete or continuous.
1. The weight of the professional boxers
2. The number of defective COVID-19 Rapid Antibody Test Kit
23
3. The area of lots in an exclusive subdivision
4. The number of recovered patients of COVID-19 per province
5. The number of students with Academic Excellence in a school per district
C. Determine the values of the random variables in each of the following
distributions.
1. Two coins are tossed. Let H be the number of tails that occur. Determine
the values of the random variable H.
2. A meeting of envoys was attended by 4 Koreans and 2 Filipinos. If three
envoys were selected at random one after the other, determine the values
of the random variable K representing the number of Koreans.
D. Construct the probability distribution of the situation below:
Two balls are drawn in succession without replacement from an urn
containing 5 white balls and 6 black balls. Let B be the random variable
representing the number of black balls. Construct the probability distribution
of the random variable B.
Additional Activities
Grace Ann wants to determine if the formula below describes a probability
distribution. Solve the following:
𝑃(𝑋) =
𝑋+1
6
where X = 0, 1, 2. If it is, find the following:
1. P(X = 2)
2. P(X ≥ 1)
3. P(X ≤ 1)
24
25
No. Frequency P(R)
of
Red
Balls
0
1
1/8
1
3
3/8
2
3
3/8
3
1
1/8
Total
8
1
No. of
Frequency P(D)
Defective
Test kit
0
1
1/8
1
3
3/8
2
3
3/8
3
1
1/8
Total
8
1
What's More
What I Can Do
A.
0, 1, 2, 3
What’s In
What’s New
1. Experiment or
trial
2.
3.
4.
5.
What I Know
A.
C.
4
8
6
36
12
B.
Sample Space
Event
Outcome
Probability
1.
2.
3.
4.
5.
1.
2.
3.
4.
5.
B.
1.
2.
3.
4.
5.
D
B
B
C
A
Continuous
Discrete
Continuous
Continuous
Discrete
1. 0, 1, 2
2. 0, 1, 2
Answer Key
26
Assessment
A.
1.
2.
3.
4.
5.
D
B
B
C
A
B.
1.
2.
3.
4.
5.
C.
1.
2.
D.
Continuous
Discrete
Continuous
Discrete
Discrete
0, 1, 2
0, 1, 2, 3
S = {WW, WB, BW, BB}
Outcomes
Additional Activities
X
0
1
2
Total
WW
WB
BW
BB
P(X)
1/6
1/3
1/2
1
1. P(X = 2) = 1/2
2. P(X ≥ 1) = 5/6
3. P(X ≤ 1) = 1/2
Value of
Variable B
0
1
1
2
1/4
2/4 or
1/2
1/4
1
1
4
2
Total
1
2
P(B)
Frequency
No. of
Black
Balls
0
1
References
Books
Belecina, R. R., Baccay, E. S., & Mateo, E. B. (2016).
Statistics and Probability. Rex Book Store.
Ocampo, J. J., & Marquez, W. G. (2016). Senior High Conceptual Math & Beyond
Statistics and Probability. Brilliant Creations Publishing, Inc.
Website
britannica.com. (2021). Retrieved from Britannica:
https://www.britannica.com/science/statistics/Random-variables-andprobability-distributions
courses.lumenlearning.com. (n.d.). Retrieved from lumen Boundless Statistics:
https://courses.lumenlearning.com/boundless-statistics/chapter/discreterandom-variables/
27
For inquiries or feedback, please write or call:
Department of Education – Region III,
Schools Division of Bataan - Curriculum Implementation Division
Learning Resources Management and Development Section (LRMDS)
Provincial Capitol Compound, Balanga City, Bataan
Telefax: (047) 237-2102
Email Address: bataan@deped.gov.ph